Consider the sequence of steps to solve the equation: 2(x − 4) + 6x = 9x − 10

Given ⇒ 2(x − 4) + 6x = 9x − 10
Step 1 ⇒ 2x − 8 + 6x = 9x − 10
Step 2 ⇒ 2x + 6x − 8 = 9x − 10
Step 3 ⇒ 8x − 8 = 9x − 10
Step 4 ⇒ 8x − 8x − 8 = 9x − 8x − 10
Step 5 ⇒ 0 − 8 = x − 10
Step 6 ⇒ −8 = x − 10
Step 7 ⇒ −8 + 10 = x − 10 + 10
Step 8 ⇒ 2 = x + 0
Step 9 ⇒ 2 = x

Which step in solving this equation is justified by the Distributive Property?
A) Step 1 ⇒ 2x − 8 + 6x = 9x − 10
B) Step 2 ⇒ 2x + 6x − 8 = 9x − 10
C) Step 3 ⇒ 8x − 8 = 9x − 10
D) Step 4 ⇒ 8x − 8x − 8 = 9x − 8x − 10

Add 8 to both sides: -4x>-12

Divide both sides by -4: x>3

Flip the sign since we divided by a negative: x<3

So the correct answer is B

Hope this helped!

Answer:

The answer is B

Step-by-step explanation:

The was done, I did the question and it is right.

Answer:

5000

Step-by-step explanation:

Answer:

Step-by-step explanation:

㏒(6)-㏒(2)=㏒(6/2)=㏒ 3

The expression log(6) – log(2) in form of log(c) is log(12).

Logarithms are another way of writing exponents in mathematics. A number's logarithm with a base equals another number. Exponentiation is the inverse function of logarithm.

A logarithm is defined as the number of powers to which a number must be increased in order to obtain some other numbers. It is the simplest way to express enormous numbers.

We have to write the expression log(6) – log(2) in form of log(c).

Using product property for logarithms

log a + log b= log (ab)

Here, a= 6 and b= 2 then

ab = 6 . 2= 12

Thus, the required form of log(6) – log(2) is log(12).

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Answer:

D

Step-by-step explanation:

5*4=20

4*5=20

Answer:

The answer is B

Step-by-step explanation:

–3 and 1; 4x and 7x

The Like terms of the given expression are 4x and 7x ; -3 and 1.

Those terms which have the same variables are raised with the same power.

For example, 5t^3 and 6t^3 are like terms since the variable is same, and it is raised to the same power 3.

Given expression;

4 x - 3 + 7 x + 1

Like terms are;

4x and 7x

-3 and 1

Thus, option C is correct.

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Step-by-step explanation:

[tex](8x - 8) \degree \: and \: (7x + 8)\degree \: are \: \\ vertically \: opposite \: angles. \\ vertically \: opposite \: angles \: are \: \\ congruent \\ \therefore \: (8x - 8) \degree \: = \: (7x + 8)\degree \\ \therefore \: 8x - 7x = 8 + 8 \\ \huge \pink{ \boxed{\therefore \: x = 16\degree}}[/tex]

Answer:

16

Step-by-step explanation:

As the angles are vertically opposite

7x + 8 = 8x - 8

x = 16

Answer:

17-3=14

37-23=14

20-6=14

Answer:

15-1=14

48-34=14

137-123=14

Step-by-step explanation:

To check work

14+1=15

14+34=48

14+123=137

Answer:

19/20

Step-by-step explanation:

3 1/5 - 2 1/4

16/5 - 9/4

64/20 - 45/20

19/20

Answer: 19/20

Step-by-step explanation:

Convert the mixed numbers to improper fractions, then find the LCD and combine.

3 1/5 becomes 16/5

2 1/4 becomes 9/4

LCD = 20

Answer:

At least 12

Step-by-step explanation:

25 percent of 150 is 37.50.  0.25 X 150

450/37.5 = 8

Answer:12

Step-by-step explanation:

Find 25% of 150 and then divide 450 with the answer of 25%.

See explanations below on solving simultaneous equations by elimination.

Step-by-step explanation:

In solving simultaneous equations by elimination, you make one side of the variables equal and eliminate that side by either addition or subtraction, then solve the remaining variable whose value is then used in one of the equations to find the other variable. For example;

(i)   4x - 2y= 10

(ii)  x+ y =4

Making the x variable part equal to eliminate x

1(4x-2y=10)--------multiply by 1

4(x+y=4) ---------multiply by 4

4x -2y =10

4x+4y=16

Apply subtraction to eliminate the x variables

0 +6y =6

6y=6

y=6/6 = 1

Use the value of y =1 in the equation x+y= 4

x+y=4

x+1=4

x=4-1 = 3

x= 3,  and y=1

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Answer:

  $2.50

Step-by-step explanation:

Jake's total expenditure is ...

  total = admission + c × (number of tickets)

  36 = 13.50 + 9c . . . an equation to solve

  4 = 1.50 +c . . . . . . . divide by 9

  2.50 = c . . . . the cost of one ticket

Each ticket cost Jake $2.50.

Answer:

[tex]g(15)=93.8\%[/tex]

see the explanation

Step-by-step explanation:

Let

x ----> the number of years since 2008,

g(x) ----> the percent of people 25 years and older who have completed at least high school

we know that

[tex]g(x)=0.008x^2+0.42x+87.5[/tex]

so

For x=15 years since 2008

substitute

[tex]g(15)=0.008(15)^2+0.42(15)+87.5=93.8\%[/tex]

That means

In the year 2023 (2008+15) the percent of people 25 and older completing at least high school will be 93.8%

Final answer:

To find g(15), we substitute x with 15 in the function g(x) = [tex]0.008x^2 + 0.42x + 87.5[/tex], yielding g(15) = 95.6%. This means that in 2023, it's projected that 95.6% of people 25 and older will have completed high school according to the given quadratic trend.

Explanation:

The student is asking for the evaluation of the function g(x) = [tex]0.008x^2[/tex] + 0.42x + 87.5 at x = 15, which represents the number of years since 2008. To find g(15), we need to substitute x with 15 in the given function:

g(15) = 0.008(15)2 + 0.42(15) + 87.5

Calculating the value step by step:

152 = 225

0.008 × 225 = 1.8

0.42 × 15 = 6.3

1.8 + 6.3 + 87.5 = 95.6

Therefore, g(15) = 95.6.

In words, this means that if the trend described by function g(x) continues, then in the year 2023 (15 years after 2008), 95.6% of people aged 25 and older will have completed at least a high school education. This is a projection of graduation rates over time.

Speed of skyler is 204 mph and speed of marcus is 212 mph

Solution:

Skyler is 104 miles away from Marcus

Therefore,

Distance = 104 miles

They meet after 4 hours

Time taken = 4 hours

Let "x" be the speed of sklyer

Marcus travels 8 mph faster than skyler

Therefore,

Speed of marcus = 8 + x

They are traveling towards each other

Since they are traveling towards each other, we can add up their speeds

Speed = x + 8 + x = 2x + 8

The distance is given by formula:

[tex]distance = \frac{speed}{time\ taken}\\\\104 = \frac{8+2x}{4}\\\\104 \times 4 = 8 + 2x\\\\8 + 2x = 416\\\\2x = 416-8\\\\2x = 408\\\\x = 204[/tex]

Thus speed of skyler = x = 204 mph

Speed of marcus = 8 + x = 8 + 204 = 212 mph

Thus speed of skyler is 204 mph and speed of marcus is 212 mph

It would take 9 people 34.5 minutes to paint 9 walls.

23 divided by 6 equals 3.83. That is how many minutes it takes one person to paint one wall. Multiply 3.83 by 9 and you get your answer, 34.5 minutes.

Answer:

Well if the deck was sown i would know butt... ill just give an example so if the height is 5 and the length 10 then you do 5 times 10 and get 50 A=50

Step-by-step explanation:

Answer:

119.5

Step-by-step explanation:

um....well i looked it up so yeah

Answer:

50

Step-by-step explanation:

Answer:

Around 30 coupons

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Correct on edge 2023

Answer:

i think n-23=x

the question is worded weirdly

Answer

49500litres

Step-by-step explanation:

Check attachment  

Answer:1

Step-by-step explanation:2+2=4

4/4=1

Answer:

ST = √353 or 18.79

I can add a step-by-step explanation if you want me to.

The length of ST is approximately 18.79 units.

The shortest distance (length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:

[tex]D = √[(x-p)² + (y-q)²] D = \sqrt{(x-p)^2 + (y-q)^2} \: \rm units.[/tex]

We are given that;

Points= S (-1,8), and T (7,-9)

Now,

x1​=−1

y1​=8

x2​=7

y2​=−9

Substituting these values into the formula, we get:

d=(7−(−1))2+(−9−8)2​

d=(8)2+(−17)2​

d=64+289​

d=353​

d= 18.79

Therefore, by the distance the answer will be 18.79 units.

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Answer:

Step-by-step explanation:

Answer:

.56 miles or 56/100 of a mile

Step-by-step explanation:

5 days = 4/10 = .4

7 days = ?

.4 / 5 * 7 = .56

.56 miles or 56/100 of a mile

Diane walked her dog 4/10 of a mile each day for 5 days. By multiplying the daily distance by the number of days, we determine that Diane walked a total of 2 miles with her dog over the week.

To determine how far Diane walked her dog over the 5 days, we need to calculate the total distance by multiplying the daily distance by the number of days she walked her dog. Diane walked her dog 4/10 of a mile each day for 5 days.

Here's how you can calculate the total distance:

Multiply the daily distance by the number of days.

So, 4/10 mile/day imes 5 days = 2/1 miles.

Therefore, Diane walked a total of 2 miles with her dog over the 5 days.

a. The inequality 15x+300≤750 represents the situation.

b. It means that the band can spend at most $30 on each uniform without exceeding the budget.

Step-by-step explanation:

Given,

Budget = $750

Competition fee = $300

Uniforms to make = 15

Let,

x be the amount for each uniform.

a.  Write an inequality to represent this situation.

Uniforms to make * Cost per uniform + Competition ≤ Budget

15x+300 ≤ 750

The inequality 15x+300≤750 represents the situation.

b.  Solve the inequality and describe what it means in the situation.

[tex]15x+300\leq 750\\15x+300-300\leq 750-300\\15x\leq 450[/tex]

Dividing both sides by 15

[tex]\frac{15x}{15}\leq \frac{450}{15}\\x\leq 30[/tex]

It means that the band can spend at most $30 on each uniform without exceeding the budget.

Keywords: inequality, division

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The inequality representing this situation is 15x + $300 <= $750. Solving for x gives x <= $30

The student is interested in determining how much the school marching band can spend on each new uniform given a specific budget constraint. To represent this situation, we need to establish an inequality.

Writing the inequality-
Let's denote the cost of one uniform as x. With 15 uniforms needed and competition fees totalling $300, the inequality that represents the budget situation is:

15x + $300 <= $750

Solving the inequality-

To solve for x, subtract $300 from both sides of the inequality:

15x <= $450

Next, divide both sides by 15:

x \<= $30

This means that they can spend at most $30 for each uniform. The inequality tells us the maximum spending cap for one uniform, ensuring the total cost for all uniforms plus competition fees does not exceed the available budget of $750.

Answer:the answer to the question "Which of the following expressions cannot be evaluated?" is (-6)^1/2 . (A)

Answer:

The answer is “A”

Please give the person brainliest above me, she deserves it. :)

Step-by-step explanation:

hi shae

Answer:

5 hours

Step-by-step explanation:

because he is working twice as fast which means he will get the job done faster

Answer:

KE = 6250 Joule.

Step-by-step explanation:

Every moving body has kinetic energy and it is given by the expression

[tex]KE = \frac{1}{2}mv^{2}[/tex]

where the moving body has m as the mass and v as the velocity.

If m is in Kg and v is in meter/sec, then KE will be expressed in Joule.

Now, in this case, m = 500 and v = 5 meter/sec.

So, [tex]KE = \frac{1}{2} \times 500 \times (5)^{2} = 6250[/tex] Joule. (Answer)

The sample space for odd numbers between 20 and 30 is {21, 23, 25, 27, 29}. These are integers that are not wholly divisible by 2.

The sample space is a term used in mathematics, specifically in statistics and probability, to describe all possible outcomes of an experiment. In this case, the experiment is to find all odd numbers between 20 and 30. An odd number is an integer that is not exactly divisible by 2. The odd numbers between 20 and 30 are: 21, 23, 25, 27, and 29. Therefore, the sample space you are looking for is {21, 23, 25, 27, 29}.

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Answer:

4 gallons

Step-by-step explanation:

86 = 23x -6

92 = 23x

x = 4

Answer:

4

Step-by-step explanation:

y=23x-6

86=23x-6

92=23x

x=92/23

x=4

Answer: -1/3

1/3+-/=-1/3